Electron Velocity Overshoot Research Articles

Mechanism of Reverse Leakage Current in Schottky Diode Fabricated on Large Bandgap Semiconductors like Ga2O3 or Diamond Part II

The bandgap of Ga2O3 (4.5-4.9 eV) is larger than the bandgap of GaN (3.4 eV). In addition, single crystal bulk Ga2O3 wafers can be more easily manufactured than GaN wafers. Therefore, Ga2O3 has strong potential for applications in high power semiconductor devices [1]. Schottky diodes fabricated on n-type Ga2O3 have strong potential as fast high-power switching devices. Similarly, the bandgap of diamond (5.5 eV) is very large and diamond Schottky diodes have good potential.One possible mechanism of reverse leakage current in Schottky diodes is image force barrier lowering at the metal-semiconductor interface. Historically, there were 2 theories regarding the image force barrier lowering effect. In 1953, Krömer published his theory that the image force dielectric constant in the equation for Schottky emission should be equal to 1 [2]. Subsequently in 1964, Sze et al. published their theory that the image force dielectric constant in the equation for Schottky emission should be equal to n2 [3], where n is the refractive index of the semiconductor in the infrared or visible light range. In 1969, Sze published a book which has influenced many scientists [4]. Sze’s theory [3]-[4] quickly became the dominating theory whereas Krömer’s theory essentially became a forgotten theory. In 2020, the author pointed out that Krömer’s theory is quite frequently more compatible with experimental results for Ga2O3 or diamond Schottky diodes [5]. In 2021, the author attempted to propose a new theory involving the concept of electron velocity overshoot to unify Krömer’s theory and Sze’s theory, as shown in Fig. 1 [6]; Krömer’s theory is better than Sze’s theory for high reverse bias voltage.In conclusion, the author pointed out that it is necessary to resurrect an old and forgotten theory from Krömer in order to explain the experimental data on the reverse leakage current of Schottky diodes fabricated on large bandgap semiconductors like Ga2O3 and diamond, etc. A theoretical basis based on quasi-ballistic transport will be provided.

A novel model of avalanche current generation in the GaN HEMT equivalent circuit

We consider the large-signal equivalent circuit of a field-effect transistor (FET) with characteristics and parameters calculated using a two-dimensional (2D) quasi-hydrodynamic model while taking into account the electron velocity overshoot. In accordance with this equivalent circuit when applied to an AlGaN/GaN high-electron-mobility transistor (HEMT), the avalanche current (in the feedback branch) is zero at all operating points. However, this contradicts the significant difference seen between the results of time-domain simulations of a radiofrequency (RF) amplifier in which the transistor is simulated using a 2D model that does versus does not include the avalanche multiplication of the charge carriers. We propose a new model for the avalanche current generation, based on such simulations including the avalanche multiplication and on the theory of impact-ionization avalanche transit-time (IMPATT) diodes. This model allows the synthesis of amplifiers with high power-added efficiency (PAE).

Mathematical aspects of simulating efficient RF operation of HEMTs

We consider the mathematical basis of our earlier developed program for the time domain analysis of the amplifier’s electrical circuit whose nonlinear part (intrinsic transistor) is given by the two-dimensional model including the electron velocity overshoot and avalanche multiplication of charge carriers. This program is quite economical (we execute it on personal computers) because we modified classical numerical methods used by us, such as the Samarskii locally one-dimensional scheme for parabolic partial differential equations and Newton method for time domain simulations.

Physical modelling and experimental characterisation of InAlAs/InGaAs avalanche photodiode for 10 Gb/s data rates and higher

InAlAs/InGaAs avalanche photodiodes (APD) were simulated using physical device models, then designed and fabricated to detect light in the wavelength range from 1.3 to 1.55 µm. DC characterisation under dark and light conditions were performed at room temperature to measure and investigate the performance of the APD. High-frequency characterisation was carried out on the device to extract the diode intrinsic and extrinsic parameters. The work reported here focuses on the dark and light physical device simulations (both under DC and AC conditions) which were accomplished using Atlas SILVACO tool. The effect of electron velocity overshoot was considered for accurate bandwidth modelling. All measured data are in excellent agreement with the modelled ones. The internal device gain of the APD is 45 at −23.5 V leading to a ∼220 GHz gain–bandwidth product. This successful APD model can be exploited to further improve the diode structure for higher data rate applications beyond 10 Gb/s.

Method for simulating efficient RF operation of HEMTs

For estimating the potential of an AlGaN/GaN HEMT, we simulate a model amplifier with this transistor in the time domain. The base of this simulation is the earlier proposed two-dimensional model of electron-hole plasma in HEMTs, which takes into account the effects of electron velocity overshoot and avalanche multiplication of charge carriers due to impact ionization. The matching elements of the amplifier are obtained by means of the intrinsic transistor large-signal equivalent circuit. Using the time domain simulations, we calculate the power-added efficiency and other amplifier parameters as functions of the maximum available power of the input RF generator at a frequency of 18 GHz. The maximum power-added efficiency of 35% is one of our results.

Short-channel transport behavior in scaled 25-nanometer GaAs/AlGaAs heterostructure field effect transistors

Ultra-short channel AlGaAs/GaAs heterostructure field effect transistors with gate lengths ranging up to 20 nm were fabricated using an electron-beam lithography process in order to examine the fundamental limitation of transistor scaling. An improvement in the transconductance caused by electron velocity overshoot starts to occur in our devices with sub-70-nm gate lengths, which is suppressed partially by a parasitic gate-fringing at a reduced gate aspect ratio. However, we find that the transconductance starts to drop for gate lengths below 40 nm and that the enhancement in the transconductance caused by the velocity overshoot is limited with further scaling. To investigate the velocity overshoot and its’ degradation, we used a transport model based on the Retarded Langevin equation (RLE). The average transient velocity obtained by using the RLE shows reasonable agreement with the effective electron velocity extracted from the experimental results by using an analytical approximation. Also, the inverse-linear proportionality of log(I DS) to {ie1} (based on the WKB approximation) demonstrates the existence of short-channel tunneling at very small gate lengths (smaller than 40 nm in our devices).

Steady-State and Transient Electron Transport within Bulk InAs, InP and GaAs: An Updated Semiclassical Three-Valley Monte Carlo Simulation Analysis

An ensemble Monte Carlosimulation is used to compare high field electron transport in bulk InAs, InP and GaAs. In particular, velocity overshoot and electron transit times are examined. For all materials, we find that electron velocity overshoot only occurs when the electric field is increased to a value above a certain critical field, unique to each material. This critical field is strongly dependent on the material, about 3 kV/cm for InAs, 10 kV/cm for InP and 5 kV/cm for the case of GaAs, We find that InAs exhibits the highest peak overshoot velocity and that this velocity overshoot lasts over the longest distances when compared with GaAs and InP. Finally, we estimate the minimum transit time across a 1 μm InAs sample to be about 2 ps. Similar calculations for InP and GaAs yield 6.6 and 5.4 ps, respectively. We find that the optimal cutoff frequency for an ideal InAs based device ranges from around 79 GHz when the device thickness is set to 1 μm. We thus suggest that indium arsenide offers great promise for future high-speed device applications. The steady-state and transient velocity overshoot characteristics are in fair agreement with other recent calculations.

Onset for the Electron Velocity Overshoot in Indium Nitride

A theoretical study on the electron drift velocity and electron nonequilibrium temperature of indium nitride (InN) is presented. It is based on a nonlinear quantum kinetic theory which provides a description of the dissipative phenomena developing in the system. The ultrafast time evolution of the electron drift velocity and electron nonequilibrium temperature is obtained, and overshoot effects are evidenced on both of them. The overshoot onsets are shown to occur at 4 kV/cm, electric field intensity which is considerably smaller than those recently derived by resorting to Monte Carlo simulations.

Electron Transport Behavior on Gate Length Scaling in Sub-50-nm GaAs Metal Semiconductor Field Effect Transistors

Short channel GaAs Metal Semiconductor Field Effect Transistors (MESFETs) have been fabricated with gate length to 20 nm, in order to examine the characteristics of sub‐50 nm MESFET scaling. Here the rise in the measured transconductance is mainly attributed to electron velocity overshoot. For gate lengths below 40 nm, however, the transconductance drops suddenly. The behavior of velocity overshoot and its degradation is investigated and simulated by using a transport model based on the retarded Langevin equation (RLE). This indicates the existence of a minimum acceleration length needed for the carriers to reach the overshoot velocity. The argument shows that the source resistance must be included as an internal element, or appropriate boundary condition, of relative importance in any model where the gate length is comparable to the inelastic mean free path of the carriers.

Monte Carlo Simulations of Electron Transport in In0.52Al0.48As/In0.75Ga0.25As High Electron Mobility Transistors at 300 and 16 K

We performed two-dimensional Monte Carlo (MC) simulations of 200-nm-gate InP-based In0.52Al0.48As/In0.75Ga0.25As pseudomorphic high electron mobility transistors (HEMTs) at 300 and 16 K to clarify the effect of temperature on electron transport. On decreasing the temperature, the calculated maximum transconductance gm increases from 1110 mS/mm at 300 K to 1400 mS/mm at 16 K. On the other hand, the calculated cutoff frequency fT increases from 168 GHz at 300 K to 223 GHz at 16 K. The electron velocity overshoot under the gate is enhanced by reducing the temperature. The resulting average electron velocity under the gate increases from 3.60×107 cm/s at 300 K to 5.26×107 cm/s at 16 K. The average velocity of the electrons and electron occupancy in each valley were calculated to clarify the trend of the electron velocity with temperature. We found that the intervalley phonon scattering as well as the intravalley scattering plays a very important role in determining the average electron velocity at 300 K. The contribution of the intervalley scattering to the average electron velocity is almost of the same degree as that of the intravalley scattering at 300 K.

Comparison of hot electron transport properties in wurtzite phase of ZnS, GaN and 6H-SiC

An ensemble Monte Carlo simulation have been carried out to study temperature and doping dependencies of electron drift velocity in ZnS, GaN and 6H-SiC. We study how electrons, initially in thermal equilibrium, drift under the action of an applied electric field within bulk of these materials. Calculations are made using a non-parabolic effective mass energy band model, Monte Carlo simulation that includes all of the major scattering mechanisms. The band parameters used in the simulation are extracted from optimized pseudopotential band calculations to ensure excellent agreement with experimental information and ab-initio band models. For all materials, it is found that electron velocity overshoot only occurs when the electric field is increased to a value above a certain critical field, unique to each material. This critical field is strongly dependent on the material parameters. Transient velocity overshoot has also been simulated, with the sudden application of fields up to 600 kVm -1 , appropriate to the gate-drain fields expected within an operational field effect transistor. The electron drift velocity relaxes to the saturation value of about 1.5×105 ms -1 within 3 ps, for all crystal structures.

Comparison of hot electron transport properties in wurtzite phase of ZnS, GaN and 6H-SiC

An ensemble Monte Carlo simulation have been carried out to study temperature and doping dependencies of electron drift velocity in ZnS, GaN and 6H-SiC. We study how electrons, initially in thermal equilibrium, drift under the action of an applied electric field within bulk of these materials. Calculations are made using a non-parabolic effective mass energy band model, Monte Carlo simulation that includes all of the major scattering mechanisms. The band parameters used in the simulation are extracted from optimized pseudopotential band calculations to ensure excellent agreement with experimental information and ab-initio band models. For all materials, it is found that electron velocity overshoot only occurs when the electric field is increased to a value above a certain critical field, unique to each material. This critical field is strongly dependent on the material parameters. Transient velocity overshoot has also been simulated, with the sudden application of fields up to 600 kVm-1, appropriate to the gate-drain fields expected within an operational field effect transistor. The electron drift velocity relaxes to the saturation value of about 1.5×105 ms-1 within 3 ps, for all crystal structures. Keywords: Ensemble Monte Carlo, drift velocity, transient velocity, pseudopotential.

Steady-state and transient electron transport within bulk ternary nitride semiconductors including GaInN, AlGaN and AlInN using a three-valley Monte Carlo method

An ensemble Monte Carlo simulation is used to compare bulk electron transport in wurtzite phase GaInN, AlGaN and AlInN materials. Electronic states within the conduction band valleys at theΓ, U and K are represented by non-parabolic ellipsoidal valleys centered on important symmetry points of the Brillouin zone. For all materials it is found that electron velocity overshoot only occurs when the electric field is increased to a value above a certain critical field, unique to each material. This critical field is strongly dependent on the material parameters. Transient velocity overshoot has also been simulated with the sudden application of fields up to ∼5×107 Vm-1, appropriate to the gate-drain fields expected within an operational field effect transistor. The electron drift velocity relaxes to the saturation value of ∼1.5×105 ms-1 with in 4 ps for all crystal structures. The steady-state and transient velocity overshoot characteristics are in fair agreement with other recent calculations. Keywords: Brillouin zone, gate-drain, transient, critical field, drift velocity, semiconductor

Steady-state and transient electron transport within bulk ternary nitride semiconductors including GaInN, AlGaN and AlInN using a three-valley Monte Carlo method

An ensemble Monte Carlo simulation is used to compare bulk electron transport in wurtzite phase GaInN, AlGaN and AlInN materials. Electronic states within the conduction band valleys at the Γ, U and K are represented by non-parabolic ellipsoidal valleys centered on important symmetry points of the Brillouin zone. For all materials it is found that electron velocity overshoot only occurs when the electric field is increased to a value above a certain critical field, unique to each material. This critical field is strongly dependent on the material parameters. Transient velocity overshoot has also been simulated with the sudden application of fields up to ~5×10 7 Vm -1 , appropriate to the gate-drain fields expected within an operational field effect transistor. The electron drift velocity relaxes to the saturation value of ~1.5×10 5 ms -1 with in 4 ps for all crystal structures. The steady-state and transient velocity overshoot characteristics are in fair agreement with other recent calculations.

Calculated electron steady-state drift velocity in lattice matched Ga0.5In0.5P and Al0.26Ga0.26In0.48P using a threevalley Monte Carlo simulation

We present calculations based on an ensemble Monte Carlo program of the steady-state electron drift velocity in bulk Ga0.5In0.5P and Al0.26Ga0.26In0.48P as well as present a list of material parameters for these substances which are of use in the modeling of semiconductor devices made from these material types. Calculations are made using a non-parabolic effective mass energy band model, Monte Carlo simulation that includes all of the major scattering mechanisms. The band parameters used in the simulation are extracted from optimized pseudopotential band calculations to ensure excellent agreement with experimental information and ab-initio band models. The effects of alloy scattering on the electron transport physics are examined. For two materials, it is found that electron velocity overshoot only occurs when the electric field is increased to a value above a certain critical field, unique to each material. This critical field is strongly dependent on the material parameters. Key words: Steady-state, pseudopotential, alloy scattering, velocity overshoot, critical field.

An Accurate and Simplified Modeling of Energy and Momentum Relaxation Rates for Metal–Oxide–Semiconductor Device Simulation

An accurate and simplified modeling for the energy and momentum relaxation rates has been proposed for simulating a velocity overshoot of electrons in metal–oxide–semiconductor field-effect transistors (MOSFETs). The relaxation rate has been featured by electron energy (w), gate field (EG), and impurity-doping concentration (NI). When the rate is defined by finv in the inversion layer and by fbulk in bulk, the relaxation rate (r) in the whole area of MOSFETs can be modeled by an envelope function; r=max ( finv, fbulk). Based on the Boltzmann equation, relation of the relaxation rate to w, EG, and NI has been studied and a simple modeling for r(w,EG,NI) has been developed. The rate can be expressed by a combination of one-dimensional data arrays. By using the simple modeling, the rate has been readily determined with the help of Monte Carlo simulation, and the validity of the rate modeling has been demonstrated by carrying out device simulation.

Effect of Gate–Drain Spacing for In0.52Al0.48As/In0.53Ga0.47As High Electron Mobility Transistors Studied by Monte Carlo Simulations

We performed two-dimensional Monte Carlo (MC) simulations of 60-nm-gate InP-based lattice-matched In0.52Al0.48As/In0.53Ga0.47As high electron mobility transistors (HEMTs) to clarify the effect of the gate–drain spacing Lgd on device performance. The calculated maximum transconductance gm and cutoff frequency fT increase with decreasing Lgd down to 50 nm, which agrees with experimental values. To explain the increase in gm and fT, we obtained electron velocity profiles in the InGaAs channel layer. Electron velocity overshoot under the gate is enhanced with decreasing Lgd. The resulting average electron velocity under the gate increases with decreasing Lgd. The enhancement of the electron velocity overshoot can be explained by using potential profiles in the HEMT. Potential profile under the gate in the InGaAs channel becomes steeper with decreasing Lgd.

Anisotropic Transient and Stationary Electron Velocity in Bulk Wurtzite GaN

The theoretical calculation of transient electron velocity overshoot in wurtzite <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</i> -axis GaN indicates a higher transient overshoot peak for transport in the basal plane ( Gamma- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> and Gamma- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> ) than along the growth direction (Gamma- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</i> ). Characteristic rise times for the transient overshoot peak are found to be shorter for transport along the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</i> -axis. Stationary electron velocity is significantly larger for transport oriented in the basal plane than along the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</i> -axis. No significant anisotropy is observed, however, in either the transient or steady-state electron velocity as a function of field orientation within the basal plane itself. The higher peak transient and stationary velocities in the basal plane are directly attributable to the anisotropy of the electronic dispersion, which exhibits lower effective mass along the Gamma- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> and Gamma- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> directions and greater nonparabolicity along the Gamma- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</i> direction.

MONTE CARLO MODELING OF HOT ELECTRON TRANSPORT IN BULK AlAs, AlGaAs AND GaAs AT ROOM TEMPERATURE

The results of an ensemble Monte Carlo simulation of electron drift velocity response on the application field in bulk AlAs , AlGaAs and GaAs are presented. All dominant scattering mechanisms in the structure considered have been taken into account. For all materials, it is found that electron velocity overshoot only occurs when the electric field is increased to a value above a certain critical field, unique to each material. This critical field is strongly dependent on the material parameters. Transient velocity overshoot has also been simulated, with the sudden application of fields up to 1600 kVm-1, appropriate to the gate-drain fields expected within an operational field effect transistor. The electron drift velocity relaxes to the saturation value of ~105 ms-1 within 4 ps, for all crystal structures. The steady state and transient velocity overshoot characteristics are in fair agreement with other recent calculations.

COMPARISON OF STEADY-STATE AND TRANSIENT ELECTRON TRANSPORT IN InAs, InP AND GaAs

An ensemble Monte Carlo simulation is used to compare high field electron transport in bulk InAs , InP and GaAs . In particular, velocity overshoot and electron transit times are examined. For all materials, we find that electron velocity overshoot only occurs when the electric field is increased to a value above a certain critical field, unique to each material. This critical field is strongly dependent on the material, about 400 kVm-1 for the case of GaAs , 300 kVm-1 for InAs and 700 kVm-1 for InP . We find that InAs exhibits the highest peak overshoot velocity and that this velocity overshoot lasts over the longest distances when compared with GaAs and InP . Finally, we estimate the minimum transit time across a 1 μm GaAs sample to be a bout 3 ps. Similar calculations for InAs and InP yield 2.2 and 5 ps, respectively. The steady-state and transient velocity overshoot characteristics are in fair agreement with other recent calculations.